Two circles of radius 4 are externally tangent to each other and are internally tangent to a circle of radius 10 at points A and B. Find the distance AB.
If we draw the centers for all the circles and connect them, we get a triangle of 8, 8, 8.
If we draw a triangle for the center of the large triangle and point A and B, we have a similar triangle with 2 sides being 10, meaning the side AB is also 10.
I think we can use the idea of similar triangles here
Call the center of the large circle O and the centers of the smaller circles = C and D
OC = (10 - 4) = 6 CD = (4 + 4) = 8
OA = 10 AB = ???
And triangles OCD and OAB are similar
CD / OC = AB / OA
8 / 6 = AB / 10
10 * 8 / 6 = AB
10 ( 4/3) = AB
40/3 = AB = 13 1/3